Temporal Links Between Preference and Perception

James McCullough, University of Arizona
Douglas MacLachlan, University of Washington
Raza Moinpour, University of Washington
ABSTRACT - This study examines the reliability of preference analysis using LINMAP in situations where perceptions are found to be stable over time. The results of preference analysis are shown to be less stable than perceptions but still reasonably reliable. Suggestions are made on the use of this type of analysis to understand consumer responses to information and persuasive communications.
[ to cite ]:
James McCullough, Douglas MacLachlan, and Raza Moinpour (1981) ,"Temporal Links Between Preference and Perception", in NA - Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Ann Abor, MI : Association for Consumer Research, Pages: 178-181.

Advances in Consumer Research Volume 8, 1981      Pages 178-181


James McCullough, University of Arizona

Douglas MacLachlan, University of Washington

Raza Moinpour, University of Washington


This study examines the reliability of preference analysis using LINMAP in situations where perceptions are found to be stable over time. The results of preference analysis are shown to be less stable than perceptions but still reasonably reliable. Suggestions are made on the use of this type of analysis to understand consumer responses to information and persuasive communications.


A major goal of promotional activity in marketing is the alteration of consumer preferences for products. In order to effectively utilize information and persuasion in promotional campaigns, it is necessary to understand how preferences are formed and what influences their change.

Marketing researchers have developed methods for examining both preference and perception. Examination of formation and change of preference would seem to necessitate examination of the link between preference and perception. Although several researchers have demonstrated the temporal reliability of measures used to measure preference and perception (Moinpour, McCullough, and MacLachlan 1976; Acito 1977; McCullough and Best 1979), attempts to link preference and perception in longitudinal studies have been limited and unsuccessful (McCullough, MacLachlan, and Moinpour 1979).

Examination of the link between perception and preference requires reliable measurement of both perception and preference, and reliable analysis of the link between the two. Individual differences scaling (INDSCAL) has been shown to be a reliable method for the analysis of consumer perceptions (Carroll and Chang 1970; Moinpour, McCullough, and MacLachlan 1976). Preference ranking is generally a reliable method for the collection of individual preferences (Acito 1977), although, as Best (1978) points out subjects need solid reference criteria to insure reliability. Linear programming techniques for the multidimensional analysis of preference judgments (LINMAP) appear to provide a suitable method for examination of the link between perception and preference (Srinivasan and Shocker 1973), but the reliability of the method has not been demonstrated.

Research Questions

This study is designed to examine the reliability of analysis of preference and perception as a tool for understanding consumer behavior. To accomplish this objective it is necessary to determine if:

1.  Perceptions of unchanged stimuli can be reliably scaled at different points in time as reported in the literature.

2.  Preferences are stable over time.

3.  Preferences and perceptions reported at different points in time for identical stimuli can be reliably linked by joint application of preference and perception analysis.

The research reported here is an attempt to establish baseline controls for the measurement of changes in consumer perceptions and preferences resulting from informational and persuasive messages.

Experimental Method

A convenience sample of twenty-five subjects drawn from undergraduate marketing classes participated in testing sessions during which they were told they were. testing the usefulness of new marketing research techniques. At each session, subjects were asked to rate all possible pairs of 10 toothpaste brands (N = 45) on nine-point dissimilarity scales and to rank the brands in order of preference. The brands used in the study were chosen to match the previous study by Moinpour, McCullough, and MacLachlan (1976). Two additional brands (Aim and Aquafresh) were included to increase constraint (see Table 1). An attempt was made to replicate the previous study as closely as possible. Subjects completed this task three times at one week intervals. Twenty-four subjects completed the study, providing responses at one week intervals over a three week period.


Pairwise dissimilarities were analyzed using the INDSCAL algorithm which produces group stimulus space coordinates and individual dimension saliences. These perceptual spaces were compared using the CMATCH algorithm (Cliff, 1966) while the preference rankings were compared using Spearman rank correlation. The group stimulus space coordinates and preferences rankings for each individual were analyzed using the LINMAP mixed mode option to produce individual dimensional weights or utilities.

Assume that each stimulus (brand) k can be represented by a vector of p coordinates

Y = (Y1, Y2, . . . , Yp)   (1)

The INDSCAL model for measuring individual perceptions assumes the basic structure of the product space is shared by all people in the relevant market, but allows individual subjects to stretch or compress that space by a set of dimension weights or saliences. The group space coordinates



by a set of dimension weights or saliences. The group space coordinates Yjk for attribute J and brand k are transformed into individual coordinates Xijk for individual 1 by the application of subject-dimension weights (saliences) Wij. The algorithm developed by Carroll and Chang (1970) simultaneously derives Yjk and Wij values from matrices of brand dissimilarities for ail individuals using the model:

Yijk = (Wij) 1/2Yjk   (2)

The LINMAP Model

The LINMAP is one of many "utility" generating algorithms. It has the advantage of modeling decreasing marginal utility and ideal points for some attributes and constant marginal utility (vector model) for other attributes. It posits the following functional form for utility of brand k at time t:


where j1 is the set of all attributes having finite ideal points and j2 is the set of all attributes with infinite ideal points; Vj is the attribute "importance" (i.e., the value of the attribute in determining preference); and Ij is the subject's ideal point on the jth dimension.

Results and Discussion

The perceptual maps derived from INDSCAL were reasonably consistent over the three week period. The group stimulus configuration is shown in Figure 1. The goodness of fit between periods 1 and 2 was .904 and between periods 2 and 3, it was .762. Distance vector correlations were .746 and .447, respectively. The slightly lower value between weeks 2 and 3 was due largely to variation in the position of Ipana, a brand not familiar to most subjects.

The Spearman rank correlation coefficients for the subject ranked preferences were uniformly high. Between weeks the value ranged between .84 and 1.00 with a mean value of .96. These results indicated subjects were clearly able to perform both the tasks leading to the development of perceptual maps and the preference rank of the stimuli with a high degree of reliability.

The coordinates of the stimulus space and the preference rankings were employed in the LINMAP algorithm to generate relative importance weights for the spatial dimensions in determining individual utilities for the attributes as they were used by the subject to determine preference. There was weak correlation between these values across the three periods. The correlation between weeks 1 and 2 was .26 and between 2 and 3 was .45.

This result is not surprising. The INDSCAL procedure develops what are in effect individual perceptual maps of the stimulus space. Although the group space may be reasonably consistent between periods there is considerable individual variation in dimensional salience as can be seen from the data in Table 2. In spite of this individual variation, the correlation between individual dimensional saliences is .75 for weeks 1 and 2 and .77 for weeks 2 and 3. In order to correct the utility values derived from LINMAP for the individual variation contained in the INDSCAL results, the utility values must be multiplied by the dimensional saliences. With their correction, the correlation between the adjusted utilities is .61 for weeks 1 and 2 and .74 for weeks 2 and 3. The values of dimensional saliences are shown in Table 2; the LINMAP-generated individual dimension utilities are shown in Table 3; and the adjusted individual dimension utilities are shown in Table 4.










The analysis of perceptions using INDSCAL appears to be reliable as was previously reported (Moinpour, McCullough, and MacLachlan 1976). The increase in the size of the stimulus set from eight to ten did not appear to alter the reliability of the scaling procedure. It was possible that inclusion of additional stimuli might have increased cask difficulty and reduced reliability. There is no evidence that this occurred. It should be noted, however, that selection of stimuli can have a noticeable effect on the stability of the map. In this case, Ipana exhibited a much larger variation than Crest; for example, Ipana is not marketed in the area of the study and may not have been familiar to many subjects--it was not used by any. Crest, on the other hand, was the most commonly used product among respondents and exhibited very little temporal movement in the scaling solutions (see Figure 1).

Expressed preferences also appear to be reliable. There is no evidence of significant temporal variation in preference ranking in this study.

The link between perceptions and preference is also quite strong. Although the temporal stability is not as high as might be desired, it is significant and indicates a reasonable consistency in the results.

The major advantage of non-metric analysis is the relative ease of data collection to yield metric output. This type of analysis assumes that sufficient constraint can be placed upon the ordinal data to insure a unique solution. This assumption presents significant problems for perceptual analysis. First, sufficient stimuli must be analyzed to insure adequate constraint. In this case, ten stimuli were used, providing sufficient constraint but requiring subjects to evaluate 45 pairs of products. In spice of this there was no evidence that subjects were unreliable in responding.

The second issue concerns the relationship between the subjects' perceptions and the group space. The INDSCAL analysis assumes the subjects utilize a common perceptual space and differ in their weighting of the dimensions. The data in Table 5 indicate this may not be true. For some subjects (subject 3, for example) the INDSCAL solution does a poor job of representing their perceptual space. When this occurs, it is not surprising that the results appear to be unreliable. In future analysis, it should be possible to identify subjects with differing perceptions and treat them separately. By doing this, the results should become more reliable.

This study has shown that INDSCAL and LINMAP can be used to jointly analyze preferences and perception. The results appear to be stable over time. Further research is needed to determine if these methods can be used to identify changes in perception and preference to provide a basis for understanding the influence of information and persuasion on the consumer.




Acito, F. (1977), "An Investigation of Some Data Collection Issues in Conjoint Measurement," Proceedings, Chicago: American Marketing Association, 82-85.

Assal, A. (1971), "Perceptual Mapping to Reposition Brands," Journal of Advertising Research, February, 39-42.

Best, R. J. (1978), "Validity and Reliability of Criterion-Based Preferences," Journal of Marketing Research, 15, 154-160.

Carroll, J. D. and Chang, J. J. (1970), "Analysis of Individual Differences in Multidimensional Scaling via n-way Generalization of 'Eckart-Young' Decomposition," Psychometrika, 35, 283-319.

Lutz, R. J. (1975), "Changing Brand Attitudes Through Modification of Cognitive Structure," Journal of Consumer Research, 11, 45-49.

MacLachlan, D. L., Moinpour, R., and McCullough, J. M. (1977), "Experimenting with Perceptual Change Strategies," Multivariate Behavioral Research, 12, 429-446.

McCullough, J., and Best, R. (1979), "Conjoint Measurement: Temporal Stability and Structural Reliability," Journal of Marketing Research, 16, 26-31.

McCullough, J. M., MacLachlan, D. L. and Moinpour, R. (1979), "Linking Preference and Perception: A Longitudinal Study," Proceedings: American Psychology Association, Division 23, September.

McGuire, W. J. (1968), "The Nature of Attitudes and Attitude Change," Handbook of Social Psychology, Addison-Wesley.

Moinpour, R., McCullough, J. M. and MacLachlan, D. L. (1976), "Time Changes in Perception: A Longitudinal Application of Multidimensional Scaling," Journal of Marketing Research, i, 245-253.

Parker, B. R. and Srinivasan, V. (1976), "A Consumer Preference Approach to the Planning of Rural Primary Healthcare Facilities," Operations Research, 24, 991-1025.

Pessemier, E. A. (1978), "Stochastic Properties of Changing Preferences," American Economic Review, 28, 380-385.

Srinivasan, V. and Shocker, A. D. (1973), "Estimating the Weights for Multiple Attributes in a Composite Criterion Using Pairwise Judgments," Psychometrika, 38, 473-493.